Abstract
We consider, in the harmonic superspace approach, the six-dimensional \( \mathcal{N} \) = (1, 0) supersymmetric Yang-Mills gauge multiplet minimally coupled to a hypermultiplet in an arbitrary representation of the gauge group. Using the superfield proper-time and background-field techniques, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. We demonstrate that in the particular case of \( \mathcal{N} \) = (1, 1) SYM theory, which corresponds to the hypermultiplet in the adjoint representation, all one-loop divergencies vanish, so that \( \mathcal{N} \) = (1, 1) SYM theory is one-loop finite off shell.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P.S. Howe and K.S. Stelle, Ultraviolet Divergences in Higher Dimensional Supersymmetric Yang-Mills Theories, Phys. Lett. B 137 (1984) 175 [INSPIRE].
P.S. Howe and K.S. Stelle, Supersymmetry counterterms revisited, Phys. Lett. B 554 (2003) 190 [hep-th/0211279] [INSPIRE].
G. Bossard, P.S. Howe and K.S. Stelle, The ultra-violet question in maximally supersymmetric field theories, Gen. Rel. Grav. 41 (2009) 919 [arXiv:0901.4661] [INSPIRE].
G. Bossard, P.S. Howe and K.S. Stelle, A note on the UV behaviour of maximally supersymmetric Yang-Mills theories, Phys. Lett. B 682 (2009) 137 [arXiv:0908.3883] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Quantum Properties of Higher Dimensional and Dimensionally Reduced Supersymmetric Theories, Nucl. Phys. B 227 (1983) 252 [INSPIRE].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained \( \mathcal{N} \) = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge, (2001).
P.S. Howe, G. Sierra and P.K. Townsend, Supersymmetry in Six-Dimensions, Nucl. Phys. B 221 (1983) 331 [INSPIRE].
P.S. Howe, K.S. Stelle and P.C. West, \( \mathcal{N} \) = 1 D = 6 harmonic superspace, Class. Quant. Grav. 2 (1985) 815 [INSPIRE].
B.M. Zupnik, Six-dimensional Supergauge Theories in the Harmonic Superspace, Sov. J. Nucl. Phys. 44 (1986) 512 [INSPIRE].
E.A. Ivanov, A.V. Smilga and B.M. Zupnik, Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B 726 (2005) 131 [hep-th/0505082] [INSPIRE].
E.A. Ivanov and A.V. Smilga, Conformal properties of hypermultiplet actions in six dimensions, Phys. Lett. B 637 (2006) 374 [hep-th/0510273] [INSPIRE].
I.L. Buchbinder, E.A. Ivanov, B.S. Merzlikin and K.V. Stepanyantz, One-loop divergences in the 6D, \( \mathcal{N} \) = (1, 0) abelian gauge theory, Phys. Lett. B 763 (2016) 375 [arXiv:1609.00975] [INSPIRE].
G. Bossard, E. Ivanov and A. Smilga, Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace, JHEP 12 (2015) 085 [arXiv:1509.08027] [INSPIRE].
I.L. Buchbinder, E.I. Buchbinder, S.M. Kuzenko and B.A. Ovrut, The background field method for \( \mathcal{N} \) = 2 super Yang-Mills theories in harmonic superspace, Phys. Lett. B 417 (1998) 61 [hep-th/9704214] [INSPIRE].
E.I. Buchbinder, B.A. Ovrut, I.L. Buchbinder, E.A. Ivanov and S.M. Kuzenko, Low-energy effective action in \( \mathcal{N} \) = 2 supersymmetric field theories, Phys. Part. Nucl. 32 (2001) 641 [Fiz. Elem. Chast. Atom. Yadra 32 (2001) 1222] [INSPIRE].
I.L. Buchbinder, E.A. Ivanov and N.G. Pletnev, Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry, Phys. Part. Nucl. 47 (2016) 291 [Fiz. Elem. Chast. Atom. Yadra 47 (2016) 541] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Supersymmetric Euler-Heisenberg effective action: Two-loop results, JHEP 05 (2007) 081 [hep-th/0703269] [INSPIRE].
I.L. Buchbinder and B.S. Merzlikin, On effective Kähler potential in \( \mathcal{N} \) = 2, D = 3 SQED, Nucl. Phys. B 900 (2015) 80 [arXiv:1505.07679] [INSPIRE].
A.A. Ostrovsky and G.A. Vilkovisky, The Covariant Effective Action in QED. One Loop Magnetic Moment, J. Math. Phys. 29 (1988) 702 [INSPIRE].
I.L. Buchbinder and N.G. Pletnev, Hypermultiplet dependence of one-loop effective action in the \( \mathcal{N} \) = 2 superconformal theories, JHEP 04 (2007) 096 [hep-th/0611145] [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, The Relaxed Hypermultiplet: An Unconstrained \( \mathcal{N} \) = 2 Superfield Theory, Nucl. Phys. B 214 (1983) 519 [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, Miraculous Ultraviolet Cancellations in Supersymmetry Made Manifest, Nucl. Phys. B 236 (1984) 125 [INSPIRE].
I.L. Buchbinder and N.G. Pletnev, Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background, Phys. Lett. B 744 (2015) 125 [arXiv:1502.03257] [INSPIRE].
I.L. Buchbinder and N.G. Pletnev, Construction of 6D supersymmetric field models in \( \mathcal{N} \) = (1,0) harmonic superspace, Nucl. Phys. B 892 (2015) 21 [arXiv:1411.1848] [INSPIRE].
I.L. Buchbinder, B.S. Merzlikin and N.G. Pletnev, Induced low-energy effective action in the 6D, \( \mathcal{N} \) = (1, 0) hypermultiplet theory on the vector multiplet background, Phys. Lett. B 759 (2016) 626 [arXiv:1604.06186] [INSPIRE].
S.M. Kuzenko and I.N. McArthur, Effective action of \( \mathcal{N} \) = 4 super Yang-Mills: \( \mathcal{N} \) = 2 superspace approach, Phys. Lett. B 506 (2001) 140 [hep-th/0101127] [INSPIRE].
S.M. Kuzenko and I.N. McArthur, Hypermultiplet effective action: \( \mathcal{N} \) = 2 superspace approach, Phys. Lett. B 513 (2001) 213 [hep-th/0105121] [INSPIRE].
S.M. Kuzenko and I.N. McArthur, On the background field method beyond one loop: A manifestly covariant derivative expansion in super Yang-Mills theories, JHEP 05 (2003) 015 [hep-th/0302205] [INSPIRE].
S.M. Kuzenko, Exact propagators in harmonic superspace, Phys. Lett. B 600 (2004) 163 [hep-th/0407242] [INSPIRE].
S.M. Kuzenko, Five-dimensional supersymmetric Chern-Simons action as a hypermultiplet quantum correction, Phys. Lett. B 644 (2007) 88 [hep-th/0609078] [INSPIRE].
P.K. Townsend and G. Sierra, Chiral Anomalies and Constraints on the Gauge Group in Higher Dimensional Supersymmetric Yang-Mills Theories, Nucl. Phys. B 222 (1983) 493 [INSPIRE].
S.M. Kuzenko, J. Novak and I.B. Samsonov, The anomalous current multiplet in 6D minimal supersymmetry, JHEP 02 (2016) 132 [arXiv:1511.06582] [INSPIRE].
I.L. Buchbinder, S.M. Kuzenko and B.A. Ovrut, On the D = 4, \( \mathcal{N} \) = 2 nonrenormalization theorem, Phys. Lett. B 433 (1998) 335 [hep-th/9710142] [INSPIRE].
I.L. Buchbinder, N.G. Pletnev and K.V. Stepanyantz, Manifestly \( \mathcal{N} \) = 2 supersymmetric regularization for \( \mathcal{N} \) = 2 supersymmetric field theories, Phys. Lett. B 751 (2015) 434 [arXiv:1509.08055] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1612.03190
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Buchbinder, I.L., Ivanov, E.A., Merzlikin, B.S. et al. One-loop divergences in 6D, \( \mathcal{N} \) = (1, 0) SYM theory. J. High Energ. Phys. 2017, 128 (2017). https://doi.org/10.1007/JHEP01(2017)128
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2017)128